Lavender Town has no gym, so you won't be able to do much here.
Later though, you can catch Ghost Pokemon in the Pokemon Tower when you get a Silph Scope. Without it, your mission in the tower won't
be complete, and all the Ghost Pokemon won't be identified. For now, you can battle Gary in the tower on the second floor. Gary's team now greatly varies
depending on who you chose for your starter at the beginning of the game. Once you get the Silph Scope, you'll find Mr. Fuji at the top of the
foggy tower, and he'll give you a PokeFlute that's used for waking up Snorlax and other Pokemon.

Now, visit the Name Rater if you want to, who'll be able to change the name of your Pokemon. Then shop for new items in
the PokeMart. Finally, go west to Route 8.